I just moved to an area where the hardness of the water is significantly higher than at my previous place of brewing. In brewing my ale recipe that use to, on average, go from O.G. 1.056 to F.G.1.012 I can now only get down to 1.020 at best. Can the difference in water chemistry be effecting these results (pH, hardness) or are there other more likely influences that I'm overlooking? My methods have been consistent so I would like to think that human error has been minimized.

If you are mashing, water can affect your process significantly. If you are using extract, then water becomes less important. If your pH is too high in your water, you will get poor conversion in your mash. This effect then cascades through the rest of the process.

I've been doing a partial mash 2-3 lbs of grains and 4-6 lbs of extract. Recently I have been increasing the amount of grains and experimenting with the mash process so your advise will help considerably. What is a good range of pH for the water?

I jsut happened to have access to the instruments necessary to measure the parameters of my tap water. Sure enough when I measured the pH it was 7.9. Haven't measured the hardness yet but I'll bet it is also too high. Then I measured the pH of a gallon of distilled water which is 6.3. Great tip! Going to use the new water source for my next batch and will post the differences is specific gravity readings for the same recipe with two different types of water.

When I brew(whole grain) a Munich-style beer I routinely use 50% distilled water and monitor ph during collection while sparging. The day before I brew I boil my sparge water to get rid of as much chlorine as possible. DON'T use all distilled water.

Good advice, but there could also be some other things happening here as well. For example, if your doing a partial mash at what temp. are you mashing at? Higher mash temps provide more unfermentables and therefore more body or less attenuation. This may seem silly, but check your thermometer. I'm sure I'm not the only one who has found that their therm. was off by a few degrees, and if your using a lab therm. the mercury can sometimes seperate. Also, are you using dry or liquid extract? Liquid extract gennerally does not ferment as completely as dry does, the key word here however is generally. How fermentable an extract is will also vary from manufacturer to manufactuer, and possibly from batch to batch. Have you switched the brand or type of extract you use? In my experience there can be a BIG difference in the fermentability from one brand to another. Finally, attenuation is also going to vary from yeast strain to yeast strain, some yeast are more attenuative than others.

I've been fighting "incomplete" fermentations for a while. What my club & I found was surprising.
First and foremost stack the odds in your favor by doing all the good things; aerate your wort, add yeast nutrient, pitch sufficient yeast, etc...
The big culprit with my (partial mash) brews turned out to be the dry malt extract I was using. Batches were finishing at 1.026 and higher. Informal tests showed that there was nothing fermentable left at that point (Champagne yeast couldn't even get it going). Several calls later it turns out vendors were reporting the same problem with that shipment of dme.
I made two batches side-by-side, one with the dme and one with comparable liquid extract. The dme batch finished at 1.026, the liquid batch at 1.014 (O.G. = 1.056).
Cheers!